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Suppose That in the Course of Testing Whether Age

question 29

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Figure
Suppose that in the course of testing whether Age and Family Size are jointly significant,you estimate the results in Figure 6.3.  SUMMARY OUTPUT  Regrestion Starittict  Muftiple R. 0.070494476 R Sequrt 0.004969471 Adigated R. Square 0.001879314 Standard Esror 4.819403326 Observations 970\begin{array}{lc}\text { SUMMARY OUTPUT }\\\\\\\hline\text { Regrestion Starittict } & \\\hline \text { Muftiple R. } & 0.070494476 \\\text { R Sequrt } & 0.004969471 \\\text { Adigated R. Square } & 0.001879314 \\\text { Standard Esror } & 4.819403326 \\\text { Observations } & 970 \\\hline\end{array}



 ANOVA dfS5MSF Signifieance F Regranion 3112.056601237.35220041.6081614420.185858614 Reaidual 96622436.9423723.22664841 Total 96922548.99897\begin{array}{l}\text { ANOVA }\\\begin{array}{lccccc}\hline & d f & S 5 & M S & F & \text { Signifieance } F \\\hline \text { Regranion } & 3 & 112.0566012 & 37.3522004 & 1.608161442 & 0.185858614 \\\text { Reaidual } & 966 & 22436.94237 & 23.22664841 & & \\\text { Total } & 969 & 22548.99897 & & & \\\hline\end{array}\end{array}


 Coeffeientt  Srandard Error  t Stat  P-value  Lower 9596 Upper 9596 Intercept 4.0499209821.0421073413.8862800640.0001087392.0048658446.094976119 Age 0.0156269840.0103654971.5073961190.1319848780.0047145040.035968471 Family Size 0.0930934630.0846023831.1003645520.2714474420.2591191030.072932177 Years of Education 0.0056420750.064745250.0871426850.9305761570.1214154760.132699626\begin{array}{lcccccc}\hline & \text { Coeffeientt } & \text { Srandard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 9596 & \text { Upper } 9596 \\\hline \text { Intercept } & 4.049920982 & 1.042107341 & 3.886280064 & 0.000108739 & 2.004865844 & 6.094976119 \\\text { Age } & 0.015626984 & 0.010365497 & 1.507396119 & 0.131984878 & -0.004714504 & 0.035968471 \\\text { Family Size } & -0.093093463 & 0.084602383 & -1.100364552 & 0.271447442 & -0.259119103 & 0.072932177 \\\text { Years of Education } & 0.005642075 & 0.06474525 & 0.087142685 & 0.930576157 & -0.121415476 & 0.132699626 \\\hline\end{array}

 SUMALARY OUTPUT \text { SUMALARY OUTPUT }

 Regrestion Staritticz  Multiple R. 0.005034034 R Square 2.53415E05 Adjuted R. Square 0.00100769 Standard Error 4.826368211 Observations 970\begin{array}{lc}\hline \text { Regrestion Staritticz } & \\\hline \text { Multiple R. } & 0.005034034 \\\text { R Square } & 2.53415 \mathrm{E}-05 \\\text { Adjuted R. Square } & -0.00100769 \\\text { Standard Error } & 4.826368211 \\\text { Observations } & 970 \\\hline\end{array}0.1151706360.115170636


 ANOVA dfSSMSF Signffeance F Regresion 10.5714253850.5714253850.0245311910.875573561 Reiidual 96822548.4275423.29383011 Total 96922548.99897\begin{array}{l}\text { ANOVA }\\\begin{array}{lccccc}\hline & d f & S S & M S & F & \text { Signffeance } F \\\hline \text { Regresion } & 1 & 0.571425385 & 0.571425385 & 0.024531191 & 0.875573561 \\\text { Reiidual } & 968 & 22548.42754 & 23.29383011 & & \\\text { Total } & 969 & 22548.99897 & & & \\\hline\end{array}\end{array}

 Coefficienty  Standard Emor  t Star  P-value  Lower 9596 Upper 9596 Intercept 4.2888256450.7329662165.8513278666.66867E092.8504398065.727211483 Years of Education 0.0098505860.0628930640.1566243610.8755735610.1135718730.133273045 Figure 6.3\begin{array}{l}\begin{array}{lcccccc}\hline & \text { Coefficienty } & \text { Standard Emor } & \text { t Star } & \text { P-value } & \text { Lower } 9596 & \text { Upper } 9596 \\\hline \text { Intercept } & 4.288825645 & 0.732966216 & 5.851327866 & 6.66867 E-09 & 2.850439806 & 5.727211483 \\\text { Years of Education } & 0.009850586 & 0.062893064 & 0.156624361 & 0.875573561 & -0.113571873 & 0.133273045 \\\hline\end{array}\\\text { Figure } 6.3\end{array}
-When testing for the joint significance of Age and Family Size (Figure 6.3) ,the appropriate test statistic is


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